Abelian variety isogeny class 2.157.abr_bdt over $\F_{157}$

• Label: 2.157.abr_bdt
• Base field: $\F_{157}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$1 - 43 x + 773 x^{2} - 6751 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.119908747976$, $\pm0.212146068484$
Angle rank:	$2$ (numerical)
Number field:	4.0.3447093.1
Galois group:	$D_{4}$
Jacobians:	$16$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18629$	$600170493$	$14975910421433$	$369169907475247749$	$9099135881730456583424$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$115$	$24347$	$3869851$	$607613875$	$95389789090$	$14976081820451$	$2351243366988631$	$369145195073126275$	$57955795548166779079$	$9099059901017008123862$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=153x^6+101x^5+89x^4+44x^3+87x^2+83x+54$
• $y^2=77x^6+4x^5+95x^4+129x^3+92x^2+72x+52$
• $y^2=101x^6+74x^5+29x^4+12x^3+151x^2+5x+76$
• $y^2=102x^6+134x^5+138x^4+120x^3+50x^2+118x+59$
• $y^2=19x^6+112x^5+86x^4+135x^3+9x^2+59x+16$
• $y^2=97x^6+155x^5+96x^4+143x^3+17x^2+145x+124$
• $y^2=84x^6+64x^5+137x^4+73x^3+96x^2+153x+31$
• $y^2=70x^6+4x^5+58x^4+62x^3+63x^2+40x+92$
• $y^2=133x^6+17x^5+47x^4+103x^3+69x^2+10x+121$
• $y^2=123x^6+87x^5+6x^4+58x^3+33x^2+127x+15$
• $y^2=154x^6+95x^5+135x^4+17x^3+63x^2+99x+135$
• $y^2=24x^6+55x^5+96x^4+115x^3+39x^2+87x+45$
• $y^2=144x^6+23x^5+55x^4+38x^3+136x^2+78x+26$
• $y^2=149x^6+68x^5+81x^4+134x^3+65x^2+95x+116$
• $y^2=120x^6+115x^5+45x^4+68x^3+109x^2+66x+139$
• $y^2=65x^6+72x^5+56x^4+4x^3+38x^2+150x+12$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The endomorphism algebra of this simple isogeny class is 4.0.3447093.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.157.br_bdt	$2$	(not in LMFDB)